When the temperature of superconductor materials are reduced below a certain value (known as the critical temperature) the resistance of the material sharply approaches zero. The discovery of this phenomenon led to the development of a number of different technologies. One of these technologies is in the digital logic field. Currently the majority of digital logic circuits are designed using transistor technology, but the superconductive phenomenon led to the development of another option for logic circuit design. These new devices constitute a family called Single-Flux-Quantum (SFQ) circuits, of which Rapid-Single Flux-Quantum (RSFQ) digital logic devices are the most popular.
In normal transistor logic, voltage states are used to indicate a logical (binary) 1 or 0. Also, the state of the circuit can be altered by saving these voltage levels inside devices such as “Flip-Flops” and “Latches”. RSFQ circuits, on the other hand, use short voltage pulses which each correspond to a Single-Flux-Quantum (SFQ) of magnetic flux. An SFQ is the fundamental unit of magnetic flux meaning that all other flux amounts are integer multiples of this value. This amount of flux is also commonly referred to as a fluxon. The indication for a logical (binary) 1 or 0 in RSFQ circuits are thus the presence or absence of these small voltage pulses. These voltage pulses can also be saved in inductive loops in order to change the state of a RSFQ digital logic circuit.
The active elements of RSFQ digital logic circuits are Josephson Junctions. In RSFQ circuits these Junctions are normally over-damped by adding a resistor in parallel to the Junction. In this specification these resistors are omitted for the sake of clarity. Josephson Junctions normally operate in a superconductive state, thus implying that they have essentially no resistance. If, however, the amount of current through these devices reach a certain level (the critical current) the Junction returns to a resistive state. As a result of this switching from superconductive to resistive state, an SFQ voltage pulse is propagated. An SFQ pulse is able to momentarily push a Junction into its resistive state, which in turn causes a voltage to form due to the current through the Junction (V=IR). Due to the over-damped nature of the Junction this voltage will again be an SFQ pulse that is propagated further along the circuit whilst the Junction returns to its superconductive state. Another parameter of the junction, the Junction phase, is closely related to the voltage over the Junction and will be used to measure if a pulse was propagated by the Junction. This propagation mechanism is often referred to as switching.
In RSFQ digital logic devices, binary representations are implemented by the presence or absence of a single magnetic fluxon. These fluxons are shuttled throughout the circuit in the form of picosecond long voltage pulses which are passed and amplified by the active elements of RSFQ circuits. These elements are over-damped Josephson Junctions. If a Junction, usually operating in its superconductive state, is biased at around 80% of its critical current value, the voltage pulse can increase the total current amount enough to cause the Junction to enter its resistive state. Due to the over-damped nature of the Junction, a 2π phase shift of the Junction is induced after which the Junction returns to its superconductive state. This 2π phase shift is associated with the passing of magnetic flux through the junction corresponding to a single flux quantum. A fluxon shuttle can thus be formed by connecting over-damped Josephson Junctions with superconductors.
As shown in FIG. 1, a current source is used to bias both Josephson Junctions to around 80% of their critical current values. The inductances represent the inductance of the connecting superconductors. A pulse entering on the input would be reproduced at the output after both Junctions switched in turn.
If the inductance of the connecting superconductor is large enough, a fluxon may be trapped inside a superconducting loop. An inductive loop can only store an integer multiple of fluxons. The value of this storage inductor is dependent on four other variables. These variables are the size of the two Junctions forming the loop as well as the bias current applied to each of the Junctions.
An example of this behaviour can be seen in the D-Flip-Flop circuit shown in FIG. 2. A pulse entering on the “Input” will cause junction B2 to switch causing the pulse to be shuttled along the circuit. The inductance of the loop B2→L2→B3 is, however, large enough to store an SFQ pulse, thus inhibiting Junction B3's ability to switch and pass the pulse on further. This stored fluxon causes an increase in current in Junction B3 due to the circulating current induced by the trapped fluxon. An SFQ pulse entering on the “Clock” input will increase the current in Junction B3 further causing it to switch to its resistive state and to pass an SFQ pulse on to the “Output” port. Junction B4 is used to guard against unwanted behaviour when no fluxon is stored inside the storage loop. Junction B4 is biased to coincide with the current direction of an entering pulse on “Clock”. If no fluxon is stored in the storage loop an SFQ pulse entering on “Clock” will cause Junction B4 to enter its resistive state before Junction B3, thus causing the SFQ pulse to escape the circuit. A stored fluxon causes a decrease in the bias current of Junction B4, allowing Junction B3 to switch before Junction B4 can reach its resistive state. In the same way Junction B1 is used to “throw out” any input pulses when a fluxon is already being stored. It is important to note that the only way to change the state of an RSFQ digital logic circuit is the storage of SFQ pulses.
The way in which flux change is calculated can be explained with reference to FIG. 3. It is assumed that the inductance of the storage loop B2→L2→B3 is large enough to store an SFQ pulse. The amount of flux currently in the loop can then be calculated by multiplying the amount of current through each component with the value of the component's inductance, using the following formula:Φ=IL
The inductance of a Josephson Junction changes with the instantaneous current through the Junction. This inductance can be approximated by:
  L  =            L      1        ⁢                  arcsin        ⁢                                  ⁢        2        ⁢        π        ⁢                  i                      I            c                                      i                  I          c                    
Where i is the instantaneous current and Ic is the Junction's critical current. Also:
      L    1    ⁢            Φ      0              2      ⁢      π      ⁢                          ⁢              I        c            where Φ0=2.0679e−15Wb.
Using this method a change in flux due to an input pulse can be identified by calculating the sum of flux changes of each component in the loop. Note also that the total amount of flux change in the loop B2→L2→L3→B4 also has to equal that of a fluxon. This is because the amount of current change in the branch of B3 has to equal the amount of current in the branch L3→B4 due to a screening current being formed that attempts to mitigate the net increase of flux in the loop B3→L3→B4. If the amount of current was not equal this would mean that some flux was being stored in the loop B3→L3→B4 which, due to the quantization of flux in superconductive circuits, is not possible.
An exception to the above situation can be seen in FIG. 4. Suppose that the inductance of the loop B2→L2→L4→B3 is not enough to store an SFQ pulse but that the inductance of the loop B2→L2→L3 is sufficient. Under normal circumstances a stored fluxon in B2→L2→L3 will have the effect that a screening current is formed in L4→B3 to try and mitigate the increase in flux in the loop L3→L4→B3. Ideally the change in flux in the branch L4→B3 should be equal to the change in flux of the branch L3 so that the net increase in flux is zero. If, however, the amount of current necessary to screen the change in net flux would cause B3 to switch, the excess current is shunted through the branch L5→B4. This has the appearance of a non-zero change in flux in the loop B3→L5→B4. This does not pose a problem however, since the measurement of any flux which is not an integer multiple of a SFQ clearly point to the storage of a flux nearby. This fluxon storage loop can thus be identified by exploring adjacent loops.
The design of RSFQ circuits is still in its infancy and very little help is available for the designer to create large, robust circuits. The method described in this document aims to allow the designer to focus on the logical aspects of his design (for example AND gates, OR gates etc.) without spending time on the electrical circuit design (Josephson Junctions, inductors, resistors).